Best Known (118−13, 118, s)-Nets in Base 3
(118−13, 118, 797166)-Net over F3 — Constructive and digital
Digital (105, 118, 797166)-net over F3, using
- 31 times duplication [i] based on digital (104, 117, 797166)-net over F3, using
- net defined by OOA [i] based on linear OOA(3117, 797166, F3, 13, 13) (dual of [(797166, 13), 10363041, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3117, 4782997, F3, 13) (dual of [4782997, 4782880, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 4783001, F3, 13) (dual of [4783001, 4782884, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3117, 4783001, F3, 13) (dual of [4783001, 4782884, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3117, 4782997, F3, 13) (dual of [4782997, 4782880, 14]-code), using
- net defined by OOA [i] based on linear OOA(3117, 797166, F3, 13, 13) (dual of [(797166, 13), 10363041, 14]-NRT-code), using
(118−13, 118, 1594334)-Net over F3 — Digital
Digital (105, 118, 1594334)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3118, 1594334, F3, 3, 13) (dual of [(1594334, 3), 4782884, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3118, 4783002, F3, 13) (dual of [4783002, 4782884, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3117, 4783001, F3, 13) (dual of [4783001, 4782884, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3117, 4783001, F3, 13) (dual of [4783001, 4782884, 14]-code), using
- OOA 3-folding [i] based on linear OA(3118, 4783002, F3, 13) (dual of [4783002, 4782884, 14]-code), using
(118−13, 118, large)-Net in Base 3 — Upper bound on s
There is no (105, 118, large)-net in base 3, because
- 11 times m-reduction [i] would yield (105, 107, large)-net in base 3, but